Resonant free platen for vibration testing of test specimens

ABSTRACT

This invention relates to a system for vibration testing of specimens usingn electro-dynamic shaker. It overcomes the various undesirable consequences which attend the existing technology and methodology, which uses a constant thickness flat plate platen, by using an inverted, truncated pyramid type of platen, with both the base and top of square-rectangular-parallelpiped shapes, attached to a cylindrical shaker head. The outer portion of the platen has a very low mass and the section modulus is very high at the line of bending thereby increasing the resonant frequency of the platen while lowering the total weight of the platen, because there is less mass around the perimeter of the platen. The optimum shape of the pyramid is determined by a means which can be expedited by use of the computer program.

GOVERNMENT INTEREST

The invention described herein may be manufactured, used and licensed by or for the Government for Governmental purposes without the payment to me of any royalties thereon.

BACKGROUND AND SUMMARY OF THE INVENTION

In order to minimize costs and maximize vibration testing utility, test economics require that, when using an electro-dynamic shaker, that as large a number of test specimens as possible be placed on the shaker. This permits a rapid accumulation of test hours, thereby gaining high statistical confidence for a given test time. However, often frequencies are induced that excite the resonant frequency of some portion of the platen (the vibrating platform) onto which the test specimens are bolted.

Those test specimens attached to the resonating portion of the platen will experience much higher stress than either the test plan requires or that of items attached to a non-resonating portion of the platen. In addition, the location of the resonating portion of the platen changes as different frequency inputs excite different spring-mass systems at their individual natural frequencies.

When, at a certain frequency, one test specimen is subjected to greater vibrational stresses than another, the test may provide erroneous failure data for test and reliability analysis. This problem can defeat the entire purpose of the test and causes confusion as to the correct classification of a vibration caused failure. This problem has existed since a large number of items have been subjected to a wide band of vibrational frequencies for the purpose of life testing.

In the past, to solve the resonant frequency problem, four methods have been used. One solution was to use a constant thickness platen thick enough to prevent resonance in the platen corner for a given band of test frequencies. This solution proved unsatisfactory because the combined weight of the test specimens and the platen weigh more than the armature of the shaker can withstand. To maintain certain accelerations at low frequencies, a high displacement is required of the shaker. As the static load is increased on the armature, it lowers from a neutral position to a position closer to its lower limit of travel. Even if the static load is such that the lower limit safety switch is not activated, there is difficulty with activation at the lower end of the frequency spectrum required by the test program.

In the second method, if the platen cannot be made thick enough, then its mounting must be reduced in size, thereby decreasing the number of specimens to be tested by a single shaker. This would add to either the test time or the number of shakers required.

In another method, the solution is to avoid vibration at those frequencies that cause platen resonance. Since each corner of the platen will have at least one resonant frequency, a minimum of four very narrow bands of frequencies will have to be deleted from the test. However, complex electronic and mechanical systems have many small components that behave as individual spring-mass systems which, in turn, have individual resonant frequencies. Elimination of those frequencies which are in narrow bands of each platen resonance results in removal of some of the critical test frequencies for certain components thereby defeating the purpose of the test.

A final solution is to make the platen from a material with high viscous damping. The system is allowed to go through the various bands of resonance but would not reach high vibration amplitudes. Materials such as high viscous magnesium and certain irons are often used to keep amplitudes low at resonance, but some overstressing of test parts results. Instead of amplitude amplification on the order of six or more, it is usually dampened to two or three, but even at these amplitudes, parts are often overstressed, yielding erroneous test results.

The current design practice is to build a square flat plate platen of constant thickness, bolted onto the top of around shaker head, which causes a corner to resonate. The cantilevered corner behaves as a triangular plate which bends beginning from the point where the outer perimeter of the shaker head contacts the bottom of the platen. The difficulty with cantilevers is that the greater the structural masses extend from the line of bending, the lower the natural frequency. In addition, there exists a direct correlation between the area moment of inertia and the resonant frequency. A constant thickness flat plate platen has both unneeded mass at the outer corners of the vibrating triangle and a small area moment of inertia at the root of the cantilevered triangle where bending begins.

The present invention overcomes the various undesirable consequences which attend the existing equipment and methodology for vibration testing by using an inverted, truncated pyramid; the outer portion of the platen has a very low mass and the section modulus is very high at the line of bending thereby increasing the resonant frequency of the platen while lowering the total weight of the platen, because there is less mass around the perimeter of the platen.

It is an object of this invention to provide equipment and methodology for vibration testing which increases the resonant frequency of the platen.

It is another object of this invention to decrease the total weight of the platen, thereby allowing higher displacements at low frequencies of excitation.

Another object of this invention is to decrease the amount of unneeded mass thereby effecting a cost savings for construction material.

Still another object of this invention therefore, is to provide a system that provides uniform vibration stresses for all specimens subjected to the test.

Another object of this invention is to provide a system for reliability testing at the lower end of the frequency spectrum.

It is another an object of this invention to provide an economic and reliable means for vibration testing of testing multiple devices at the same time, thereby decreasing test time and the number of shakers otherwise required.

Still another object of this invention is to provide a method for testing at all critical test frequencies without elimination of any test frequencies.

It is another object of this invention to provide a system for vibration testing without overstressing of test parts.

Further objects and advantages of this invention will become more apparent in light of the following drawings and description of the preferred embodiment of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top view of an embodiment of the vibration system;

FIG. 2 is a side view of the embodiment shown in FIG. 1;

FIG. 3 is a 45 degree side view of the embodiment shown in FIG. 1;

FIGS. 4 to 6 illustrate the top, side, and 45 degree side, respectively, of a prior art platen; and

FIGS. 7 to 12 show schematics of the calculation steps for determining the optimum platen shape.

DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION

Referring to FIGS. 1, 2, and 3 of the drawings, there is a vibration testing system shown embodying the principles of this invention. The embodiment of the invention consists of a platen 20 for material testing in the shape of an inverted pyramid 22, shaped into a square-rectangular parallellepiped configuration to receive test material on the top surface 24 and the shaker head 26 on the bottom (base) 28. The top 24 is of sufficient thickness to provide the necessary thread depth for bolting down test specimens and the bottom 28 provides a surface for mounting the platen 20 onto the shaker head 26. In FIG. 2, there is illustrated the platen from a side view.

The design of the platen 20 is accomplished by solving Equation (1), as set forth below, through two iteration processes.

Equation (1) is: ##EQU1## where: f_(n) =Natural frequency in Hertz;

E=Young's Modulus of Elasticity of platen material in pounds per square inch;

φ=Angle of the slope of the pyramid measured from the case along the edge formed by any two sides that come together up to the apex, in degrees, shown in FIG. 1;

W=Weight of the cornermost test specimen, fixture/adapters, and bolt heads, in pounds;

A=Platen area displaced by the cornermost test specimen and its fixturing, in square inches;

ρ=Density of platen material, in pounds per cubic inch; and

C=Distance from platen corner to shaker head, in inches.

Equation (1) was derived by using the Raleigh Method of natural frequency calculation. It involves the solution of a fourth order differential equation and requires a rigorous application of mechanics of materials.

The use of Equation (1) for determination of the optimum shape of the platen requires an iteration process of changing the angle φ until a desired f_(n) is found, which is the highest frequency used in a particular test program. This gives the basic shape of the platen 20. An example of the basic platen shape is shown in FIG. 7. After the basic shape is determined, a flat top surface 24 is added to the pyramid 22 as shown in FIG. 8 to provide a thread depth for bolting specimens down that are near the wedged edges of the platen 20.

FIG. 9 has dashed lines showing the projection of the pyramid to a new larger size, which increases the length of the pyramid side using trigonometry. Equation (1) is iterated again to a larger angle φ because the resonant frequency drops when the size of the platen is increased. After completion of this second iteration, the platen shape will appear as in FIG. 10.

Since the dimensions shown in FIG. 10 are awkward for fabrication purposes, it is necessary to calculate the angle of the pyramid's sides with respect to its various sides, not its corner. Equation (2) provides this transformation.

Equation (2) is:

θ=ARCTAN (√2 tan φ)

Finally, the pyramid 22 is truncated and a base 28 is added for mating with the shaker head 26. This is shown in FIG. 12.

The fabrication of the vibration testing system will now be described. Only two materials are normally used for platen fabrication, namely, aluminum and magnesium. The latter is preferred because of its lower density (about 30% lower than aluminum) and its favorable high viscous damping characteristics. However, aluminum is less costly than magnesium, therefore, if test emphasis is not placed on weight and damping, then aluminum is an economic alternative to magnesium.

Because of the large mass of metal and minimal machining required for drilling and threading of holes for bolting the platen 20 to the shaker head 26 and the test specimen to the platen top 24, casting is the least expensive method of platen fabrication.

For any test program, after determination of the specimen arrangement on the platen top 24, and measurment of the specimen and adapter weights, the computer program designs the platen 20 using the steps illustrated in FIGS. 7 to 12. This program, for computing the optimum design parameters for an inverted truncated pyramid type of platen for holding test specimens during vibration testing, is set forth as follows: V,10/999 

What is claimed is:
 1. A resonant free platen system for vibration testing of test specimens, comprising: a cylindrical shaker head, an inverted truncated pyramid platen having an area for receiving specimens to be tested and coupled to said cylindrical shaker head, and means for vibrating said shaker head.
 2. A resonant free platen system for vibration testing of test specimens as recited in claim 1, wherein said truncated pyramid platen has a form comprising a truncated square pyramid with its larger base joined to a truncated cube, all as one piece.
 3. A system as in claim 1 wherein said truncated pyramid has respectively a top square cross-sectional area and a bottom square cross-sectional area of smaller side dimension, which said bottom and top area are plane parallel to one another.
 4. A system as in claim 3 wherein test specimens are fastened at said top area, and the shaker head attached at said bottom area.
 5. A system as in claim 4 wherein said platen is formed of aluminum.
 6. A system as in claim 4 wherein said platen is formed of magnesium. 